Agreeing to agree and Dutch books

We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsi...

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Bibliographic Details
Published in:Games and economic behavior 2015-09, Vol.93, p.108-116
Main Authors: Chen, Yi-Chun, Lehrer, Ehud, Li, Jiangtao, Samet, Dov, Shmaya, Eran
Format: Article
Language:English
Subjects:
Agency theory
Agreement theorem
Agreements
Belief & doubt
Common knowledge
Common prior
Dutch book
Economic behaviour
Economic theory
Empirical research
Game theory
Information
Knowledge
Management science
No trade theorem
Principal-agent theory
Studies
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Summary:We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent's information partition is finite. •We study the possibility of agreeing to agree with multiple agents.•We propose a notion called Dutch book.•We characterize agreeing to agree in terms of Dutch books in a finite state space.•We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2015.08.002